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- W2040889710 abstract "A module M is said to satisfy the C 12 condition if every submodule of M is essentially embedded in a direct summand of M. It is known that the C 11 (and hence also C 1) condition implies the C 12 condition. We show that the class of C 12-modules is closed under direct sums and also essential extensions whenever any module in the class is relative injective with respect to its essential extensions. We prove that if M is a -module with cancellable socle and satisfies ascending chain (respectively, descending chain) condition on essential submodules, then M is a direct sum of a semisimple and a Noetherian (respectively, Artinian) submodules. Moreover, a C 12-module with cancellable socle is shown to be a direct sum of a module with essential socle and a module with zero socle. An example is constructed to show that the reverse of the last result do not hold." @default.
- W2040889710 created "2016-06-24" @default.
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- W2040889710 date "2009-02-12" @default.
- W2040889710 modified "2023-09-26" @default.
- W2040889710 title "Modules Whose Submodules are Essentially Embedded in Direct Summands" @default.
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- W2040889710 doi "https://doi.org/10.1080/00927870802248688" @default.
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